Frequency discriminator

ABSTRACT

A cross product is determined for a received signal. A dot product is also determined for the received signal. If the cross product is greater than a predetermined threshold, the cross product is decremented by the product of the dot product multiplied by a constant value. If the cross product is greater than or equal to the predetermined threshold, the cross product is incremented by the product of the dot product multiplied by the constant value. The incrementing or decrementing is continued until the frequency error approaches a minimum value.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates generally to communications. Particularly, the present invention relates to frequency discrimination in a communications environment.

[0003] 2. Description of the Related Art

[0004] CDMA communications systems typically use directional antennas located in the center of a cell and broadcasting into sectors of the cell. The antennas are coupled to base stations that transmit control the cells. The cells are typically located in major metropolitan areas, along highways, and along train tracks to allow consumers to communicate both at home and while traveling.

[0005] Even though both a mobile and a base station are transmitting on a frequency that is known to each, there are factors such as multipath errors and Doppler shift in the frequency that introduce errors in the frequency that is received. For example, if a mobile is approaching a base station, the Doppler effect increases the signal's frequency as observed by the base station. If the mobile is moving away from the base station, the base station observes a signal having a frequency that is less than the frequency transmitted by the mobile. The amount of frequency shift is a function of the speed of the mobile.

[0006] Another source of frequency error is the fact that the two local oscillators (one at the base station and one at the mobile that are used for generating the “clock” signal) can never be operating at exactly the same frequency. Typically, the mobile uses a less expensive local oscillator that can introduce a frequency error of up to 10 KHz when the carrier frequency is around 2 GHz.

[0007] During communication, the base station transmits a pilot channel that is received by the mobile. The pilot channel, comprised of pilot symbols, contains no information. The mobile utilizes the pilot symbols to generate time, frequency, phase, and signal strength references.

[0008] In some systems, the mobile also transmits a pilot signal. The mobile's pilot signal is then similarly used by the receiving base station to generate time, frequency, phase, and signal strength references relative to the mobile.

[0009] In order for a base station to communicate with a mobile on a certain frequency, both need to use a frequency discriminator in a frequency-tracking loop.

[0010]FIG. 1 illustrates a typical prior art frequency-tracking loop (FTL) 100. This figure shows a signal, Δf, entering a summer 101. Δf represents the frequency error present in an incoming signal of successive pilot symbols. The summer 101 subtracts from Δf an initial estimate Δ{circumflex over (f)}.

[0011] Frequency discriminator 105 is known and operates on the frequency error associated with successive pilot symbols. The value of each pilot symbol is herein represented by variable y_(k). The period of each symbol y_(k) is denoted by T_(S).

[0012] An incoming sequence of pilot symbols are accumulated after input signal rotation to result in a residual frequency error, out of summer 101, equal to Δf_(res). A pilot symbol y_(k) having residual frequency error Δf_(res) ^(k) may be denoted as:

y _(k) =Ae ^(j2πT) ^(_(s)) ^(Δf) ^(_(res)) ^(k) +n _(k)

[0013] where n_(k) is the additive noise corrupting the k^(th) symbol and A is a complex amplitude that is a function of, among other things, the current channel attenuation. It is assumed that fading is slow enough so that successive symbols have roughly the same complex amplitude.

[0014] A time constant (τ) is herein defined as the time it takes FTL 100 to converge to 1/e of an initial frequency error. A pull-in range conventionally defines a maximum initial frequency error for which FTL 100 is able to converge. A design goal is to minimize time constant τ, all the while maximizing the pull-in range, to maintain the standard deviation of the frequency error under steady-state conditions to within desirable levels.

[0015] A loop filter L(z) 110, series coupled to the output of frequency discriminator 105, is used to adjust the time constant τ, pull-in range, and standard deviation of the frequency error.

[0016] A known type of frequency discriminator 105 is a cross product discriminator, the operation of which may be expressed as Δf_(res) ^(cp)=imag(y_(k)y_(k-1)*), with * denoting complex conjugation. From the above equation for y_(k) and Δf_(res) ^(cp) we get

Δf _(res) ^(cp) =|A| ² sin(2πT _(s) Δf _(res))+n,

[0017] with n being a noise component. Thus as Δf_(res) approaches 1/2T_(s), the value of sin(2πT_(s)Δf_(res)) becomes smaller, resulting in the following condition:

[0018] First, the pull-in range of the FTL 100 is smaller than a theoretical pull-in range due to the effects of noise. Second, when the initial frequency error Δf is greater than ½ the theoretical pull-in range, FTL 100 takes a long time to converge to 1/e of an initial frequency error Δf.

SUMMARY OF THE INVENTION

[0019] The invention encompasses a process and apparatus for improved frequency discrimination. In particular, the invention provides a frequency tracking loop (FTL) providing a large effective pull-in range and fast convergence characteristics when an initial frequency error greater than ½ a theoretical pull-in range is detected.

[0020] In an embodiment, a cross product is first determined on an input to the FTL. This cross product is of form imag(y_(k)y_(k-1)*), where y_(k) is one sample or symbol of the received signal and y_(k-1) is a preceding symbol. A dot product, expressed as real(y_(k)y_(k-1)*), is then also determined.

[0021] When the cross product is greater than a predetermined threshold, the cross product is decremented by the product of the dot product multiplied by a predetermined constant value. In a specific implementation, a predetermined threshold of value zero and a predetermined constant value in the range of 0 to 5 are selected.

[0022] Conversely, when the cross product is less than the selected predetermined threshold, the cross product is incremented by the product of the dot product multiplied by the predetermined constant value. The calculation of and incrementing and decrementing of the cross product is generated by a frequency discriminator. The output of the frequency discriminator is used to derive a residual frequency error for an incoming signal comprised of successive pilot symbols. Successive symbols signals are fed into the frequency discriminator and the previously derived residual frequency error used to adjust the output of the frequency discriminator that then provides a new output to the FTL.

BRIEF DESCRIPTION OF THE DRAWINGS

[0023]FIG. 1 is a general block diagram of a known frequency-tracking loop (FTL).

[0024]FIG. 2 shows a more detailed block diagram of the frequency discriminator in FIG. 1, constructed in accordance with the present invention.

[0025]FIG. 3 shows a block diagram of a mobile station incorporating a FTL including the frequency discriminator of the present invention.

[0026]FIG. 4 shows a block diagram of a base station incorporating a FTL including the frequency discriminator of the present invention.

[0027]FIG. 5 shows a plot of the response of the frequency discriminator of the present invention compared to a known frequency discriminator.

[0028]FIG. 6 shows a plot of the residual frequency and a first initial frequency error as a function of time, assuming a first pilot strength, derived using the frequency discriminator of the present invention.

[0029]FIG. 7 shows another plot of the residual frequency error as a function of time, assuming a second pilot strength and the first initial frequency error, derived using the frequency discriminator of the present invention.

[0030]FIG. 8 shows a plot of the residual frequency error as a function of time, assuming a second initial frequency error, and the first pilot strength.

[0031]FIG. 9 shows a plot of the residual frequency error as a function of time, assuming a second/third initial frequency error, and the second pilot strength.

[0032]FIG. 10 shows a block diagram of a frequency discriminator for use with signals having low signal-to-noise ratios.

DETAILED DESCRIPTION

[0033] A frequency discriminator characterized by the following description provides a large effective pull-in range and fast convergence in comparison to known cross-product discriminators.

[0034] In accordance with an embodiment, the frequency includes both a simple cross product discriminator and a dot product discriminator. As used above, the cross product discriminator, denoted as cp, is expressed as:

cp=imag(y _(k) y _(k-1)*)

[0035] where y_(k) is the k^(th) pilot symbol in a renewed signal and y*_(k-1) is the complex conjugate of the k^(th)−1 pilot symbol.

[0036] A dot product discriminator, denoted as dp, by convention is expressed as:

dp=real(y _(k)y_(k-1)*)

[0037] From the above, a frequency discriminator in accordance with an embodiment, to be derived in further detail below shall be expressed as: Δ{circumflex over (ƒ)}^(new) _(res) = cp when (dp < θ) if (cp > 0), then Δ{circumflex over (ƒ)}^(new) _(res) = Δ{circumflex over (ƒ)}^(new) _(res) −α · dp else Δ{circumflex over (ƒ)}^(new) _(res) = Δ{circumflex over (ƒ)}^(new) _(res) +α · dp end end

[0038] where α and θ are constants whose values are design parameters based on a desired system.

[0039] In a first embodiment, α is in the range of 0 to 5. For α=0 the frequency discriminator collapses to a simple cross product discriminator. This can be seen by substituting 0 for α in the above expression for Δ{circumflex over (f)}_(res) ^(new).

[0040] In another embodiment, a is chosen to be a power of 2. This is derived in a frequency discriminator hardware-specific implementation where multiplication with α, where α is a power 2, becomes a simple left shift operation.

[0041] In one embodiment, θ is in the range of a real number that is less than 0. However, other ranges for θ can be used as well.

[0042] It should be further appreciated that the frequency discriminator operation described herein maybe implemented by a digital signal processor (DSP). Also, the dot product measurement may be calculated in parallel with the cross product measurements using hardware. The “if” statements can be implemented as multiplexers which use the sign bits of the cp and the dp calculation as output selectors.

[0043] A hardware block diagram of one embodiment of the frequency discriminator is illustrated in FIG. 2. Those skilled in the art will recognize that alternate embodiments may encompass different hardware variations to arrive at the same desired result.

[0044] The frequency discriminator of FIG. 2 includes a cross product block 201 and a dot product block 202. Both blocks 201 and 202 receive as inputs, sequential pilot symbols y_(k) and y_(k-1).

[0045] In the illustrative embodiment, the output cross product generated by cross product block 201 is a real value (as opposed to a complex value). The real value is expressed as cp=real(y_(k))real(y_(k-1))+imag(y_(k))imag(y_(k-1)).

[0046] The output dot product block (202) also generates a real value. This value is expressed as dp=imag(y_(k))real(y_(k-1))−real(y_(k))imag(y_(k-1)).

[0047] Output cross product (cp) is fed to the new (0) input of the first multiplexer 235, as shown. In the present example, when α=0, a simple cross product is output by the frequency discriminator 105.

[0048] Output dot product (dp) is fed to the zero (0) input of a first multiplier 215 where it gets multiplied by α. The output of the first multiplier 215 is input to a second multiplexer 225. The output of the first multiplier 215 is also input to a second multiplier 220 where the sign of the αdp signal gets inverted by multiplying the input with −1. The output of second multiplier 220 is also input to the second multiplexer 225. A select input of second multiplexer 225 is received from decision block 205.

[0049] When the output from decision block 205 is true, (i.e., cp<0), a logic high is generated and the non-inverted αdp signal is output from multiplexer 225. When not true, i.e. cp>0, the inverted αdp signal is output by multiplexer 225.

[0050] The second multiplexer 225 output is coupled to summer 230 and either αdp or (−αdp) is added to output. The output from summer 230 is input to one (1) input of first multiplexer 235.

[0051] Referring to the bottom of FIG. 2, the output of decision block 210 outputs a logic high when the condition dp<θ holds true. A logic high signal as a select input to the first multiplexer 235, will cause the first multiplexer 235. This is to select the output of summer 230. When the dot product is 0, the condition is false and the cross product is selected as the output to first multiplexer 235, and decision block 210 selects the 0 input of the first multiplexer 235.

[0052] It should be understood that the above-described signal selection process may be implemented in various programming languages. In one embodiment, the process can be implemented in the “C” programming language, and is expressed by: if(dp<θ) if(cp>0) cp−=alpha*dp; else cp+=alpha*dp; end end.

[0053] The exemplary frequency discriminator can be used in any situation that requires a low-complexity frequency estimator, such as in the frequency-tracking loop of FIG. 1. In one embodiment, the frequency discriminator is used in a FTL in a mobile communication device such as a mobile telephone. In a mobile telephone, the frequency discriminator is used on the downlink direction of the communication, i.e. the base station to mobile link.

[0054] Because the signal-to-noise ratio (SNR) of a downlink pilot is relatively high, a frequency discriminator as described above is particularly desirable.

[0055] The above frequency discriminator can also be used on the uplink direction, i.e., the mobile-to-base station link. In the uplink, the SNR of a pilot is very low. For example, a pilot SNR (E_(c)/I_(O)) might be as low as −38 dB. Frequency discriminators described above may be used in a low SNR uplink.

[0056] However, compensating for the low SNR to adjust lower SNR, it might be desirable to increase the accumulation length of the pilot symbols (i.e., increase Ts). Alternatively, low-pass filtering the cross product and the dot product will also work. Using such an embodiment changes the above equations. Factoring in a low SNR, a frequency discriminator for use in an uplink for example may be expressed as follows: cp₀ = imag(y_(k)y^(*) _(k−1)) dp₀ = real(y_(k)y^(*) _(k−1)) cp = (1 − β)cp + βcp₀ dp = (1 − β)dp + βdp₀ Δ{circumflex over (ƒ)}^(new) _(res) = cp if (dp < θ) if(cp > 0) Δ{circumflex over (ƒ)}^(new) _(res) = Δ{circumflex over (ƒ)}^(new) _(res) −α · dp else Δ{circumflex over (ƒ)}^(new) _(res) = Δ{circumflex over (ƒ)}^(new) _(res) +α · dp end end

[0057] where β is constant between 0 and 1 and the cp and dp terms are outputs of one-tap IIR filters. For very low pilot SNRs, a β closer to 0 is best. For β=1, the above expression yields the same discriminator result as the high SNR frequency discriminator expression described earlier.

[0058]FIG. 10 illustrates a frequency discriminator in an embdodiment of the present invention as might be found on the uplink of a communication system. This block diagram is not discussed in detail since it is substantially similar to the frequency discriminator of the downlink as illustrated in FIG. 2. However, the frequency discriminator for the uplink incorporates a one-tap IIR filter 1001 at the output of the cross product generator and a second one-tap IIR filter 1005 at the output of the dot product generator. Filters 1001 and 1005 are responsible for low-pass filtering the cross products and dot products, respectively.

[0059] A block diagram of a mobile station incorporating the frequency discriminator of the present invention is illustrated in FIG. 3. The mobile station includes of a transmitter 302 and receiver 301 coupled to an antenna 303. Transmitter 302 modulates the aural signals from the microphone 305 for transmission. Depending on the type of communication device, transmitter 302 or like device may digitize the aural signal from a microphone 305 prior to modulation. Antenna 303 then radiates the signal to the intended destination.

[0060] Receiver 301 incorporates an FTL 301′ constructed as described herein. Receiver 301 is responsible for receiving and demodulating signals received over antenna 303. FTL 301′ is used within receiver 301 to lock the receiver on to a desired received frequency. In some communication devices, the receiver may be responsible for converting received digital signals into their analog equivalent for transmission by a speaker 306.

[0061] The communication device is controlled by a controller 304 such as a microprocessor or other controlling device. The controller is coupled to and controls the transmitter 302 and receiver 301 functions.

[0062] A display 307 and keypad 308 are coupled to the controller 304 for displaying information entered by a user on the keypad 308. For example, the user may enter a telephone number using the keypad 308 that is displayed on the display 307 and subsequently transmitted to a base station using the transmitter 302.

[0063] In one embodiment, the communication device is a cellular radiotelephone incorporating the frequency discriminator of the present invention. Alternate embodiments include personal digital assistants with communication capabilities and computers with communication capabilities such that they are required to lock on to a desired frequency using an FTL.

[0064] A block diagram of a base station incorporating the frequency discriminator as described herein is illustrated in FIG. 4. The base station is comprised of a transmitter 401 that receives a signal from the network to which the base station is coupled. The transmitter 401 modulates the signal and transmits the signal, at the proper power level, over the antenna 405.

[0065] A received signal is received by the antenna 405 and distributed to the receiver 403 having a frequency discriminator 403. Receiver 403 tracks the frequency of the received signal using FTL 403 and demodulates any appropriate signals. The demodulated signals are sent over the network that is coupled to the base station to the appropriate destination.

[0066] In one embodiment, the base station illustrated in FIG. 4 operates in a cellular environment. Alternate embodiment base stations can be any base station that allows a mobile, wireless communication device to communicate with a fixed infrastructure.

[0067]FIG. 5 illustrates a plot of the frequency response of a frequency discriminator in accordance with an embodiment operation under various values of a. More specifically a plot of Δ{circumflex over (f)}_(res) ^(new) is shown using T_(s)=²⁵⁶/3.84×10⁶ sec. and assuming no noise. The curve corresponding to α=0 represents a regular cross-product discriminator. It can be seen from FIG. 5 that when α=2, the discriminator output closely approximates f(2πT_(s)Δf_(res))=2πT_(s)Δf_(res) and can be assured from this that we have a very efficiently performing frequency-tracking loop. For each of the curves of FIG. 5, θ is assumed to be of value zero (0).

[0068] The output of the illustrative embodiment frequency discriminator is large for values of Δf_(res) larger than half a pull-in range. The small value cross discriminator results of conventional solutions are ignored. The present frequency discriminator provides a larger effective pull-in range while also converging very fast when an initial frequency error is large.

[0069] FIGS. 6-9 illustrate results from simulations using a frequency discriminator as described herein. In each simulation, the pilot symbol accumulation length is assumed to be N=256 chips. This results in a T_(s)=²⁵⁶/3.84×10⁶ seconds, which is equivalent to a theoretical pull-in range of ±7.5 kHz.

[0070]FIG. 6 illustrates a plot of residual frequency error, f, as a function of time generated by each of two different frequency discriminators, one a conventional cross product frequency discriminator and the other a frequency discriminator as described herein. An initial frequency error of 7.4 kHz and pilot SNR of E_(C)/I_(O)=−26 dB is assumed.

[0071] It can be seen that, with the assumed initial frequency error, a conventional cross product discriminator will cause the FTL output to diverge. On the other hand, an FTL using a frequency discriminator of a present embodiment converges relatively quickly.

[0072]FIG. 7 illustrates what happens when the pilot strength is increased to E_(C)/I_(O)=−20 dB. While both present invention and prior art FTLs eventually converge, the presently disclosed frequency discriminator converges substantially faster than a cross product discriminator.

[0073] The plots of FIGS. 8 and 9 are similar to FIGS. 6 and 7 respectively. FIG. 8 better illustrates residual frequency error as a function of time with a pilot SNR of E_(C)/I_(O)=−26 dB. FIG. 9 illustrates frequency error with a pilot SNR of E_(C)/I_(O)=−20 dB. In both FIGS. 8 and 9, the initial frequency error is changed to 7.0 kHz. From these plots, it can be quickly seen how present embodiment frequency discriminator yields converges results that are substantially faster than conventional cross product discriminators.

[0074] The frequency discriminator of the present invention is not limited to any various embodiments of the specific air interface. One implementation utilizes an embodiment in a wideband code division multiple access (WCDMA) system. One skilled in the art would readily recognize that the invention has utilized any number of varying air interfaces such as general CDMA system, cdma2000, FDMA, and TDMA.

[0075] In summary, the frequency discriminator of the presently described embodiment is a relatively low complexity frequency estimator that can be used in any system requiring frequency estimation. By using dot product calculations, either in isolation or in combination with dot product measurements, results in an improved solution requiring only comparisons, additions, and simple multiplications at best.

[0076] It should be noted that in all the embodiments described above, method steps can be interchanged without departing from the scope of the invention.

[0077] Those of skill in the art will understand that information and signals may be represented using any of a variety of different technologies and techniques. For example, data, instructions, commands, information, signals, bits, symbols, and chips that may be referenced throughout the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or particles, optical fields or particles, or any combination thereof.

[0078] Those of skill will further appreciate that the various illustrative logical blocks, modules, circuits, and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate this interchangeability of hardware and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.

[0079] The various illustrative logical blocks, modules, and circuits described in connection with the embodiments disclosed herein may be implemented or performed with a general purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.

[0080] The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor such the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC. The ASIC may reside in a user terminal.

[0081] In the alternative, the processor and the storage medium may reside as discrete components in a user terminal. The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded with widest scope consistent with the principles and novel features disclosed herein. 

1. A method of providing frequency discrimination of a received input signal characterized by a receive frequency that is offset from a transmit frequency by a frequency error, the method comprising: identifying a cross product and a dot product from the received input signal; comparing the value of the cross product relative to a predetermined threshold; and adjusting the cross product by an adjustment amount equivalent to a product of the dot product times a constant value on the basis of the comparison.
 2. The method of claim 1, wherein identifying the cross product involves multiplying an imaginary portion of a product of a sample of the received input signal with a complex conjugate of a sample of a previous sample of the input signal.
 3. The method of claim 1, wherein the predetermined threshold is zero.
 4. The method of claim 1, wherein the adjusting is repeated until the frequency error is decreased to a minimum value.
 5. The method of claim 1, wherein the constant value is substantially in the range of 0 to
 5. 6. The method of claim 1, wherein the constant value is a value larger than
 0. 7. The method of claim 2, wherein the dot product is substantially equivalent to a real portion of the product of the sample of the input signal multiplied with the complex conjugate of the sample of the previous sample of the input signal.
 8. A method of converging a frequency error of a signal, characterized by a plurality of symbols, to a predetermined frequency, comprising: identifying a cross product and a dot product from the signal; multiplying the dot product by a constant value to generate a frequency adjustment product; when the cross product is greater than zero, decreasing the cross product by the frequency adjustment product; and when the cross product is less than zero, increasing the cross product by the frequency adjustment product.
 9. The method of claim 8, wherein identifying the cross product involves calculating imag(y_(k)y_(k-1)*) where y_(k) is a symbol of the plurality of symbols.
 10. The method of claim 8, wherein identifying the dot product involves calculating real(y_(k)y_(k-1)*) where y_(k) is a symbol of the plurality of symbols.
 11. The method of claim 8, wherein the steps of decreasing and increasing the cross product are repeated until the frequency error is at a minimum value.
 12. The method of claim 11, wherein the minimum value is approximately zero frequency error.
 13. A frequency discriminator apparatus having an input signal comprising a plurality of symbols, the apparatus comprising: a cross product generator, coupled to the input signal, for generating a cross product of the input signal; a dot product generator, coupled to the input signal, for generating a dot product of the input signal; a multiplier coupled to the dot product generator for generating a product in response to the dot product and a constant value; a first multiplexing device having a first input coupled to the product and a second input coupled to a negative of the product, the second multiplexer selecting as an output one of either the first input or the second input in response to the cross product; a summer coupled to the cross product generator and the output of the first multiplexing device, the summer generating a summation signal of the cross product and the product; and a second multiplexing device having a first input coupled to the cross product generator and a second input coupled to the summer, the second multiplexing device selecting as an output one of either the cross product or the summation signal in response to the dot product.
 14. The apparatus of claim 13, further including: a first comparator coupled to the cross product generator, the first comparator generating a first selection signal in response to the relation of the cross product to a first threshold value, the first selection signal coupled to a selection input of the first multiplexing device; and a second comparator coupled to the dot product generator, the second comparator generating a second selection signal in response to the dot product, the second selection signal coupled to a selection input of the second multiplexing device.
 15. The apparatus of claim 14, wherein the first threshold value is substantially zero and the second threshold value is substantially in the range of a real number less than zero.
 16. A mobile communications device comprising: a receiver for demodulating a received signal that was received over a communications channel, the receiver having a frequency discriminator that estimates a frequency of the demodulated signal, the frequency discriminator comprising: a cross product generator, coupled to the input signal, for generating a cross product of the input signal; a dot product generator, coupled to the input signal, for generating a dot product of the input signal; a multiplier coupled to the dot product generator for generating a product in response to the dot product and a constant value; a first multiplexing device having a first input coupled to the product and a second input coupled to a negative of the product, the second multiplexer selecting as an output one of either the first input or the second input in response to the cross product; a summer coupled to the cross product generator and the output of the first multiplexing device, the summer generating a summation signal of the cross product and the product; and a second multiplexing device having a first input coupled to the cross product generator and a second input coupled to the summer, the second multiplexing device selecting as an output one of either the cross product or the summation signal in response to the dot product.
 17. The mobile communications device of claim 16, further comprising: a speaker for converting the demodulated signal to an aural signal; a microphone for generating the output signal; a display that displays mobile communications data; and a controller coupled to the receiver and the display in order to control the mobile communications device.
 18. The mobile communications device of claim 16, further comprising a transmitter for modulating a code division multiple access output signal over the channel.
 19. The mobile communications device of claim 16, wherein the received signal is a code division multiple access signal.
 20. In a base station receiver adapted for use in a wireless communications network, a frequency discriminator for estimating a frequency of a received signal, the frequency discriminator comprising: a cross product generator, coupled to the input signal, for generating a cross product of the input signal; a dot product generator, coupled to the input signal, for generating a dot product of the input signal; a first low pass filter, coupled to the cross product, for generating a filtered cross product; a second low pass filter, coupled to the dot product, for generating a filtered dot product; a multiplier coupled to the filtered dot product generator for generating an adjustment product in response to the filtered dot product and a constant value; a first multiplexing device having a first input coupled to the product and a second input coupled to a negative of the adjustment product, the second multiplexer selecting as an output one of either the first input or the second input in response to the filtered cross product; a summer coupled to the filtered cross product generator and the output of the first multiplexing device, the summer generating a summation signal of the filtered cross product and the adjustment product; and a second multiplexing device having a first input coupled to the first low pass filter and a second input coupled to the summer, the second multiplexing device selecting as an output one of either the filtered cross product or the summation signal in response to the filtered dot product.
 21. A frequency tracking loop for tracking a frequency of a signal, the frequency having a frequency error, the frequency tracking loop comprising: a summer that generates a residual frequency error by subtracting a current estimate of the residual frequency error from the frequency error; and a frequency discriminator coupled to the residual error, the frequency discriminator generating the current estimate of the residual frequency error, the frequency discriminator comprising: means for determining a cross product of the residual error; means for determining a dot product for the residual error; means for decrementing the cross product by an adjustment amount equivalent to a product of the dot product of the input signal times a constant value if the cross product is greater than a predetermined threshold; and means for incrementing the cross product by the adjustment amount if the cross product is greater than or equal to the predetermined threshold.
 22. The frequency tracking loop of claim 21, further including a loop filter that couples the frequency discriminator to the summer.
 23. A frequency discriminator apparatus having an input signal comprising a plurality of symbols, the apparatus comprising: a cross product generator, coupled to the input signal, for generating a cross product of the input signal; a dot product generator, coupled to the input signal, for generating a dot product of the input signal; a first low pass filter, coupled to the cross product, for generating a filtered cross product; a second low pass filter, coupled to the dot product, for generating a filtered dot product; a multiplier coupled to the filtered dot product generator for generating an adjustment product in response to the filtered dot product and a constant value; a first multiplexing device having a first input coupled to the product and a second input coupled to a negative of the adjustment product, the second multiplexer selecting as an output one of either the first input or the second input in response to the filtered cross product; a summer coupled to the filtered cross product generator and the output of the first multiplexing device, the summer generating a summation signal of the filtered cross product and the adjustment product; and a second multiplexing device having a first input coupled to the first low pass filter and a second input coupled to the summer, the second multiplexing device selecting as an output one of either the filtered cross product or the summation signal in response to the filtered dot product. 